4. Experimental verification of the electromechanical co-simulation model of ball screw feed drive system

The electromechanical co-simulation model in this chapter has been tested on a single-axis ball screw drive system test bench shown in Figure 12. The test bench uses an i5 CNC system and

Figure 12. Single-axis ball screw feed drive test bench.

transformation. idref and iqref are compared with the feedback id and iq, respectively, and the current controller calculates the given voltages Ud and Uq of the d and q axes; then, they are converted into U<sup>α</sup> and U<sup>β</sup> in the α β coordinate system by Park inverse transformation. Finally, the SVPWM module generates six-phase PWM to drive the three-phase inverter. The inverter outputs ABC three-phase voltage to servomotor stator, which generates rotating magnetic field and produces magnetic torque on the servomotor rotor. This magnetic torque is the output torque TM of the servomotor and drives the rotor to rotate under the dynamic

Based on the lumped mass model of ball screw feed system and the servo control system simulation model, an electromechanical co-simulation model of the ball screw feed drive system was constructed. The co-simulation schematic is shown in Figure 10; as described above (a) is the semi-closed-loop cascade control system simulation model, while (b) is the lumped mass model of ball screw feed system. The inverter outputs ABC three-phase voltage to servomotor stator, which generates rotating magnetic field and produces magnetic torque on the servomotor rotor. This magnetic torque is the output torque TM of the servomotor and

The electromechanical co-simulation model of the ball screw feed drive system is shown in Figure 11. The S\_Cal module on the left side generates the trajectory command for the feed drive system according to the acceleration/deceleration strategy. Under the cascade control system, which consists of position controller, velocity controller, and current controller, the

The electromechanical co-simulation model in this chapter has been tested on a single-axis ball screw drive system test bench shown in Figure 12. The test bench uses an i5 CNC system and

servomotor drive and the ball screw accomplish the motion command accordingly.

4. Experimental verification of the electromechanical co-simulation

3.4. Electromechanical co-simulation modeling of ball screw feed drive system

Figure 11. Electromechanical co-simulation model of half-closed ball screw feed system.

drives the rotor to rotate under the dynamic relations as shown in Eq. (8).

model of ball screw feed drive system

relations of ball screw feed system.

52 New Trends in Industrial Automation

servo system of Shenyang Machine Group, which use a semi-closed-loop cascade control structure. The specifications of the test bench are listed in Table 1, which are either obtained from the manufacturers' catalogs, approximated from prior knowledge, or calculated from computer-aided design (CAD). According to the modeling method described in Chapter 2, the lumped mass model of this ball screw feed system test bench was built up. The equivalent parameters of the lumped mass model were calculated by using the specifications in Table 1, and the other calculated lumped parameters are listed in Table 2.

Taking the servomotor torque as input and the axial acceleration of work table as output, the frequency response characteristics of the lumped parameter model of the test bench are analyzed. The bode diagram is shown in Figure 13, and simulation result shows that the work table has four-order natural frequencies, which are 26.2, 76.7, 247, and 633 Hz. Further study shows that 76.7 Hz is the main axial vibration frequency of the work table, 26.2 Hz is the main axial vibration frequency of the base, and 247 and 633 Hz are the rotational vibration frequencies.


Table 1. Specifications of the test bench.


Using the same operation parameters as set in the simulation model, a feed motion experiment was conducted and the work table position was measured. The simulation results are compared to the experimental results. Figures 14 and 15 exemplarily show simulated and measured

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Figure 14. Reference velocity and feedback velocity.

Figure 15. Detailed reference velocity and feedback velocity.

Table 2. Calculated parameters used in the lumped mass model of test bench.

Figure 13. Bode diagram of the lumped parameter model of ball screw feed system.

To establish the simulation model of servo control system, the servomotor parameters are needed as shown in Table 3.

In order to compare and verify the simulation results with the experimental results, the motion command parameters and the control parameters of the experimental test and simulation are set in Table 4.


Table 3. Parameters of the servomotor.


Table 4. Motion command parameters and the control parameters settings.

Using the same operation parameters as set in the simulation model, a feed motion experiment was conducted and the work table position was measured. The simulation results are compared to the experimental results. Figures 14 and 15 exemplarily show simulated and measured

Figure 14. Reference velocity and feedback velocity.

To establish the simulation model of servo control system, the servomotor parameters are

Parameter of the component Value Parameter of the component Value Screw equivalent mass MS (kg) 11.28 Equivalent rotary inertia of screw JS (kg � <sup>m</sup>2) <sup>1</sup>:<sup>7</sup> � <sup>10</sup>�<sup>3</sup>

Axial rigidity of base KB (N=m) <sup>1</sup> � <sup>10</sup><sup>8</sup> Contact rigidity of the screw nut Kn (N=m) <sup>9</sup>:<sup>8</sup> � 107

) <sup>3</sup>:<sup>14</sup> � <sup>10</sup><sup>3</sup>

Axial rigidity of screw Kax (N=m) <sup>0</sup>:<sup>743</sup> � <sup>10</sup><sup>8</sup> Rotary rigidity of screw Krot (<sup>N</sup> � <sup>m</sup> � rad�<sup>1</sup>

Table 2. Calculated parameters used in the lumped mass model of test bench.

Figure 13. Bode diagram of the lumped parameter model of ball screw feed system.

In order to compare and verify the simulation results with the experimental results, the motion command parameters and the control parameters of the experimental test and simulation are

Parameter name Value Parameter name Value Rated power ð Þ kW 4.4 Number of pole pairs 4 Rated torque ð Þ N � m 18.6 Stator resistance per phase ð Þ Ω 1.44 Rotor inertia kg � <sup>m</sup><sup>2</sup> <sup>6</sup>:<sup>75</sup> � <sup>10</sup>-3 Inductance Ld, Lq ð Þ <sup>H</sup> <sup>8</sup>:<sup>15</sup> � 10-3

Rated speed ð Þ r=min 1500 Permanent magnetic flux ψfð Þ wb 0.21

Parameter name Value Parameter name Value Position instruction ð Þ mm 400 Position loop gain kp 50 Maximum velocity ð Þ mm=s 400 Velocity loop gain kv 10 Maximum acceleration mm=s<sup>2</sup> 2000 Current loop gain ki 30

needed as shown in Table 3.

54 New Trends in Industrial Automation

Table 3. Parameters of the servomotor.

Maximum jerk mm=s<sup>3</sup> 20,000

Table 4. Motion command parameters and the control parameters settings.

set in Table 4.

Figure 15. Detailed reference velocity and feedback velocity.

Author details

References

2011;60:779-796

154-159

Journal. 2009, Oct:130-134

Lanzhou University of Technology; 2012

Manufacture. 2001;41(9):1323-1345

Engineering. 2012;6(2):205-211

tural Machinery. 2015;46(12):370-377

Liang Luo and Weimin Zhang\*

\*Address all correspondence to: iamt.tongji.edu.cn

School of Mechanical Engineering, Tongji University, Shanghai, China

CIRP Annals–Manufacturing Technology. 2012;61:351-354

servo system. Electric Machines and Control. 2012, Jan;16(1):79-84

[1] Altintas Y, Verl A, et al. Machine tool feed drives. CIRP Annals–Manufacturing Technology.

Electromechanical Co-Simulation for Ball Screw Feed Drive System

http://dx.doi.org/10.5772/intechopen.80716

57

[2] Verl A, Frey S. Improvement of feed drive dynamics by means of semi-active damping.

[3] Dietmair A, Verl A. Drive based vibration reduction for production machines. Science

[4] Ming Y, Hao H, Dianguo X. Cause and suppression of mechanical resonance in PMSM

[5] Jian-Ren S. Research on ACC/DEC Control and Contour Error of CNC System. Lan Zhou:

[6] Erkorkmaz K, Altintas Y. High speed CNC system design. Part I: Jerk limited trajectory generation and quintic spline interpolation. International Journal of Machine Tools and

[7] Sato R. Development of a feed drive simulator. Key Engineering Materials. 2012;516:

[8] Frey S, Dadalau A, Verl A. Expedient modeling of ball screw feed drives. Production

[9] Okwudire EC, Altintas Y. Hybrid modeling of ball screw drives with coupled axial, torsional and lateral dynamics. Journal of Mechanical Design. 2009;131:071002-1-071002-9

[10] Liang L, Weimin Z, Mingjian Z, et al. Dynamics modeling and simulation of ball screw feed drive based on lumped mass model. Transactions of the Chinese Society for Agricul-

Figure 16. Frequency contents of work table acceleration.

reference velocity and feedback velocity of the servomotor at the given operating conditions. The simulation result has a similar curve to the experimental result.

Figure 16 shows frequency contents of the work table acceleration signals from simulation result and the experimental result. Comparing the simulation result with the experimental result, the co-simulation model of ball screw feed drive system can predict the vibration that occurs in the feed operation. Both results show that in this case the second-order natural frequency (about 75 Hz) but not the first-order natural frequency is the main factor influencing the performance of feed drive system.
